Effective Temperatures of Red Supergiants Estimated from Line

2 D. Taniguchi et al. genitor (e.g. Fraser et al. 2011; Smartt 2015). Moreover, the Chiavassa et al.(2011b) and Davies et al.(2013) found that accuracy of Teff directly affects that of chemical abundances the TiO-band strength depends not only on Teff and the of RSGs, which could trace the abundance distribution of luminosity but also on the temperature structure, which is young stars in the Milky Way and nearby galaxies, leading significantly affected by granulation. to the galactic evolution theory (Patrick et al. 2017; Alonso- A promising way to circumvent the problems raised so Santiago et al. 2019; Origlia et al. 2019). Hence importance far is to use signals like weak atomic lines from the pho- of accurately determining Teff of RSGs with observations tosphere defined by the optical continuum or its outside cannot be overstated. close vicinity, given that they are expected to be less af- However, the accuracy of the reported Teff of RSGs is fected by some of the above-mentioned factors (Davies et al. still under debate. Interferometry and lunar occultation are 2013; Tabernero et al. 2018). A few works have presented the two simplest ways to measure Teff of nearby stars, but Teff of RSGs estimated on the basis of photospheric signals, these methods are subject to uncertainties in some or all of e.g., the SED of wavelengths less contaminated by molecu- the following three issues: (1) limb darkening (Dyck & Nord- lar lines (the SED method; Davies et al. 2013), equivalent gren 2002; Chiavassa et al. 2009), (2) the complex extended widths of some strong atomic lines in the J band (the J - envelope called MOLsphere (Tsuji 2006; Montargèset al. band technique; Davies et al. 2015) and some atomic lines 2014) and (3) interstellar reddening (Massey et al. 2005; around the Calcium triplet (Tabernero et al. 2018). In these Walmswell & Eldridge 2012). A more recent and improved three works Teff of common RSGs in the Magellanic Clouds way is to measure the stellar radius at continuum wave- were derived. Nevertheless some systematic offsets are ap- lengths to circumvent the effects of the MOLsphere with the parent between their results, possibly due to chemical abun- spectro-interferometric technique (e.g. Ohnaka et al. 2013; dances, contamination from some molecular lines to the sig- Arroyo-Torres et al. 2013); however, the result is still affected nals and/or some effect of strong lines which is in part by limb darkening and possibly uncertainty in interstellar formed in upper layers of the atmosphere. Moreover, the reddening unless it is negligible. departure from the 1D LTE condition may be important Another type of method to estimate Teff of the RSG in RSGs (e.g. Bergemann et al. 2012b; Kravchenko et al. is to model-fit molecular bands in relatively low-resolution 2019). Most of the above works assumed the 1D LTE, and spectra in the optical (e.g. Scargle & Strecker 1979; Oestre- this shortcoming could contribute to the offsets. icher & Schmidt-Kaler 1998). The reliability of this ap- Considering these discrepancies and the aforementioned proach has been improved thanks to the advancements of factors that possibly add some systematic error to the tem- the model of the stellar atmosphere such as, most notably, peratures estimated in most of the past methods, we here the MARCS model with improved handling of molecular take a different method that satisfies the following three con- blanketing (Gustafsson et al. 2008). The most comprehen- ditions. First, the method should use only relatively weak sive work of this approach was presented by Levesque et al. atomic lines that are not severely contaminated by molecu- (2005) for RSGs in the Milky Way, in which they made use of lar lines. Such lines do not originate in atmospheric layers far the optical TiO bands (see also Levesque et al. 2006; Massey above the photosphere, where the temperature structure is et al. 2009; Massey & Evans 2016, where RSGs in other not well constrained and moreover is expected to show vari- galaxies were studied with the same method); their method ability. Second, the method should be independent of stellar is hereafter referred to as the TiO method. parameters, abundances and reddening of both interstellar A similar approach is to compare photometric colours and circumstellar origins as much as possible. Third, ideally, of RSGs with the prediction of the MARCS model (e.g. the method should be independent of uncertainties in theo- Levesque et al. 2005; Drout et al. 2012; Neugent et al. 2012), retical models, in particular with regard to the factors orig- in which molecular lines are taken into account to calculate inating from the parameters in the upper atmosphere lay- the spectral energy distribution (SED) of the RSG. This ers. Therefore, we use the `line-depth ratio' (LDR) method, approach tends to give a lower Teff in literature than the which relies on the empirical calibration of the relations be- TiO method by up to ∼ 200 K (Levesque et al. 2005, 2006), tween the LDR and Teff and satisfies the above-mentioned and hence there remain systematic uncertainties in fitting three requirements. In the next subsection, we explain what molecular absorption in optical spectra (Davies et al. 2013). the LDR and LDR-method are and review relevant past Alternatively some authors estimated Teff and spec- studies. tral types of RSGs from molecular CO, H2O, OH and/or CN lines in near-infrared spectra (e.g. Carr et al. 2000; 1.2 Line-depth ratio as an indicator of the effective Cunha et al. 2007; Origlia et al. 2019). However, Lan¸con temperature et al.(2007) and Lan¸con & Hauschildt(2010) found that the strengths of the CN molecular bands and the ratios of In cool stars (with a temperature of the solar tempera- the strengths of the CO bandheads could not be reproduced ture or lower), the depths of low-excitation lines of neu- with modern models of the static photosphere for the CNO tral atoms tend to be sensitive to Teff whereas those of abundances as predicted by stellar evolution models and a high-excitation lines are relatively insensitive (Gray 2008a). −1 microturbulent velocity (vmicro) of 2 km s . Therefore, the ratios of the depths between the low- and The temperature estimated on the basis of molecular high-excitation lines (that is, the LDRs) are good tempera- bands are affected more or less by a few factors, including ture indicators (Gray & Johanson 1991; Teixeira et al. 2016; chemical abundances and discrepancy between the atmo- López-Valdivia et al. 2019, and references therein). The basic sphere of the real star and that estimated with a simpli- procedure is as follows: (1) search high-resolution spectra for fied static model assuming one-dimensional local thermody- the line pairs whose depth ratios are sensitive to Teff , (2) es- namic equilibrium (LTE) without MOLsphere. For example, tablish the empirical relations between LDRs and Teff for MNRAS 000,1{19 (2020) Teff of RSGs using LDRs of Fe i lines in YJ bands 3 stars with well-determined Teff and (3) apply the relations mine their Teff in an unprecedented accuracy as non-spectro- to target objects to determine their Teff . interferometric measurements (Section 4). We focus on the near-infrared Y and J bands. These bands host a relatively small number of molecular lines in the RSG spectra (Coelho et al. 2005; Davies et al. 2010), and we can find sufficiently many atomic lines that are not 2 OBSERVATIONS AND REDUCTION contaminated by molecular lines (see Section 3.1 for detail 2.1 Sample and real examples). Taniguchi et al.(2018, hereafter Paper I) recently investigated LDRs in the Y and J bands of ten red We consider two groups of targets for this work. The first giants with well-determined effective temperatures (3700 < group consists of nine well-known red giants and are used for Teff < 5400 K). They calibrated 81 LDR{Teff relations with calibration of the LDR{Teff relations in this work. Five of the neutral atomic lines of various elements, and found that these stars (e Leo, Pollux, µ Leo, Aldebaran and a Cet) were a precision of ±10 K is achievable in the best cases, i.e., selected from Gaia benchmark stars (Blanco-Cuaresma et al. high-resolution spectra of early M-type red giants with a 2014), whose Teff were well constrained with interferometry good signal-to-noise ratio (S/N). This precision rivals those by Heiter et al.(2015). The other four stars are well-studied achieved in the previous results in which the LDRs in optical nearby red giants selected from the MILES sample (Sánchez- high-resolution spectra were employed (e.g. Kovtyukh et al. Blázquez et al. 2006). The temperatures of these stars were 2006). determined using the ULySS program (Koleva et al. 2009) Although Paper I gave well-defined LDR{Teff relations by Prugniel et al.(2011) with the MILES empirical spec- for solar-metal red giants, some significant systematic un- tral library as a reference. The temperature scale of Prugniel certainty remains in their work, where a simple relation be- et al.(2011) relies on the compilation of literature stellar pa- tween the LDR and Teff was assumed to hold universally. In rameters, for which most spectroscopic works assumed the reality, LDRs depend on other stellar parameters than Teff , 1D LTE condition, and we have checked the consistency be- even though Teff is the dominant parameter that determines tween the temperature scale of Prugniel et al.(2011) and the LDR of a neutral atom. Jian et al.(2019), for example, that of Heiter et al.(2015) as follows.

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